I seriously doubt there was any selection on the number of chromosomes. It just happens that we have 23 pairs.
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nicoAug 30 '12 at 12:55

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For info, all apes are known to have 48 (total), but monkeys vary (e.g. Rhesus monkeys have 42, but Capuchin monkeys have 54!). See the wiki list of chromosome counts here.
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LukeAug 30 '12 at 14:37

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@nico Sure, but there was certainly (some) selection on conserving the number. Normally, large-scale mutations such as chromosome fusions are immediately fatal and even when they are not they potentially prevent procreation with individuals which don’t have that mutation. So at least superficially there should be quite strong selective pressure to preserve ploidy.
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Konrad RudolphAug 30 '12 at 16:15

@Konrad Rudolph: but you are not selecting for the number of chromosomes, just for a configuration "that works".
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nicoAug 30 '12 at 16:26

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@nico Sure. What I meant was: given that our close ancestors had a different number of chromosomes, when/why did it change? That’s an interesting question, and essentially what OP is asking.
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Konrad RudolphAug 30 '12 at 16:36

3 Answers
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I think the OP is asking why we have one less chromosome pair than chimpanzees (for example) [23 pairs instead of 24].

The is an abundance of evidence, as alluded to above by shigeta, that human chromosome 2 is the result of a telomere-to-telomere fusion of two ancestral chromosomes (IJdoet al., 1991). This event did not occur in our closest ancestors, hence we have one less chromosome pair. In fact the sequence of human chromosome 2 contains the relic of an ancestral telomere-telomere fusion (IJdoet al., 1991).

This is a good Youtube video that discusses this, in the context of evidence for evolution. It's from a presentation given by Ken Miller about the Dover "intelligent design" trial. The whole presentation is here.
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amrJul 4 '13 at 13:55

It seems to me this answers the 'how' question but not the 'why' question. I would guess the answer to 'why' is random chance but there could be a selective advantage? Is there any evidence either way?
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Jack AidleyMay 20 '14 at 10:47

From their origin, these chromosomes underwent the following rearrangements to give rise to current human chromosomes: centromeric fission of the two submetacentrics in ancestors of all primates (∼80 million years ago); fusion of the HSA19p and HSA19q sequences, originating the current HSA19, in ancestors of all simians (∼55 million years ago); fusions of the HSA16p and HSA16q sequences, originating the current HSA16 and the two components of HSA7 before the separation of Cercopithecoids and Hominoids (∼35 million years ago); and finally, pericentric and paracentric inversions of the homologs to HSA7 after the divergence of orangutan and gorilla, respectively. Thus, compared with HSA16 and HSA19, HSA7 is a fairly recent chromosome shared by man and chimpanzee only.

@nico is right. the number of chromosomes is the result of an evolutionary timeline, puncutated by sometimes spontaneous events which shape the DNA.

These events occur in the course of evolution:

1) Chromosomal rearrangements. Large sections of the genome can flip around or become integrated in other chromosomes. By homologous recombination, regions of the genome can clip themselves out or duplicate themselves as well. If you look at the alignment of human to say chimp, there are many segments that move relative to each other.

2) chromosomal breaking or combination. Two smaller chromosomes may combine to form a larger one, or a larger one may break into two smaller chromosomes. An example of this is human chromosome 2, which is found as two smaller chromosomes in the great apes (see figure in wikipedia). We infer that this is a combination event exclusive to humans by comparing the other apes on the evolutionary tree. Birds and reptiles tend to have lots of chromosomal breakage, even to the point where the number of microchromosomes (less than 20 million bases). Mammals tend to be more conservative and not allow viable chromosomal breaks - chickens have 78 chromosomes to our 23..

3) idiomatic chromosomal behavior. Sex determining chromosomes are examples of chromosomes where a pair becomes distinctly different in size and composition.
Another example is in trypanosome which has many tiny DNA segments which code for variant surface coat proteins.

4) @rwst points, what I clean forgot, that occasionally (like maybe just a few times) there have been whole genome duplications. This can be identified by chromosomal alignments within a single genome and has not happened very often since we became eukaryotic metazoans. Not sure how many times, but perhaps just once or twice in our lineage. If anyone knows about animals/humans that would be great. As you can see the link shows whole genome duplications in plants, which don't seem care how many chromosomes there are. Plants have polyploidy, you see, so such duplication events are much better tolerated. On the other hand plants can't play video games.

You can see that these events happen at particular moments and help shape the species and the composition of the chromosomes. It is not a priori possible to predict the number or type of chromosomes just by looking at an animal, but only by looking at the related animals.

Fungi and Plants have even more variations in chromosomal composition than animals.

Also, I think it is important to note that a certain mutation in chromosome number may, indeed, be selected, because it is associated to some other advantageous phenotype. The change in chromosome number will then also be selected, but only as a "side effect".
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nicoAug 30 '12 at 13:47

segmental rearrangements that might reflect a change in the chromosomal structure can change the phenotypes and organismal behavior quite a bit. its a significant factor in the evolution of bacteria.
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shigetaAug 31 '12 at 4:07